Lax Lean Archive

Proof of `Hadamard automata and Hadamard-finite series` (4th statement)

groundedproofs/Lax619925Proofs/Hadamard.lean · lax-619925

What this proof establishes

thm✓Lax619925.Hadamard (4th statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

The commutativity problem is decidable for Hadamard-finite series over a finite alphabet (paper §5). This is the meta-theorem (EffectivePrevarietyCommutativityDecidableEffectivePrevarietyCommutativityDecidable) applied to hadamardEffectivePrevarietyhadamardEffectivePrevariety, the effective prevariety of Hadamard-finite series: its boolean decider on a presentation AA decides IsCommutative(hadamardEffectivePrevariety.semA)IsCommutative (hadamardEffectivePrevariety.sem A), and since hadamardEffectivePrevariety.semA=A.recognisedhadamardEffectivePrevariety.sem A = A.recognised, it decides IsCommutative(A.recognised)IsCommutative (A.recognised).